Notes I have taken during first year

Understanding

Go through lecture notes and understand them

Active Recall

This is the process of remembering things and bringing it forward to your mind. It is known to an effective way of remembering information.

Spaced Repetition

- Efficient way of keeping information in your mind. Space out the recalling of that information over time. Spend less time studying and retain better. - Interrupt the forgetting curve by revisting learnt materials.

2 Modes: Focus-Mode thinking vs Diffuse-mode thinking

- Focus-mode when you are actively engaged in ideas. - Diffuse-mode when you are sub-conciously thinking about the ideas.

Flashcards

- Only make flashcards of what you **understand**. Create flashcards for **important** **content**: theorems, proofs, remarks, lemmas, corollary .etc. - **Review** flashcards regularly. - **Understand** the ideas ****before you make the flash cards.

Sleep/Fitness

- Good sleep leads to good memory retention. - Fitness helps with physical and mental wellbeing.

Definition

A definition in mathematics is a precise statement delineating and naming a concept by relating it to previously defined concepts or such undefined concepts as "number" or "set".

Theorem

Theorems are the relationship between concepts and general problems which can be proved. They are important results which show how to make concepts solve problems or give major insights into the workings of the subject. They often have involved and deep proofs.

Proposition

Propositions give smaller results often relating different definitions to each other or give an alternative forms of the definition. Proofs of propositions are often less complex than the proofs of theorems.

Lemma

Lemmas are technical results used in the proofs of theorems which makes the proofs for theorem shorter.

Corollary

Corollaries are immediately followed by theorems by either giving special cases or highlighting the interest or importance of the theorem.

How to solve difficult math problems?

- Look up whatever you don't know/not sure about such as notations, symbols, words etc. Don't start the questions unless you understand they are asking/mean. - Look over your notes for ideas to be applied to the questions. - Use examples, apply the question to simple examples. - Simplify the questions. - Make sure you're focused whilst doing the problems and when you take a break you can go into diffuse-mode. - **Einstellung effect** - this refers to prexisting knowledge impedes one's ability to reach an optimal solution. We become unable to consider other solutions when we think we already have one. This is why it is important to take light breaks.

Ryan's advice

Ryan’s advice Understand everything, lecture notes, do questions provided. Do past papers and understand what you don’t understand.